// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#include "main.h"
#include <Eigen/Eigenvalues>
#include <limits>

template<typename MatrixType>
void
verifyIsQuasiTriangular(const MatrixType& T)
{
	const Index size = T.cols();
	typedef typename MatrixType::Scalar Scalar;

	// Check T is lower Hessenberg
	for (int row = 2; row < size; ++row) {
		for (int col = 0; col < row - 1; ++col) {
			VERIFY(T(row, col) == Scalar(0));
		}
	}

	// Check that any non-zero on the subdiagonal is followed by a zero and is
	// part of a 2x2 diagonal block with imaginary eigenvalues.
	for (int row = 1; row < size; ++row) {
		if (T(row, row - 1) != Scalar(0)) {
			VERIFY(row == size - 1 || T(row + 1, row) == 0);
			Scalar tr = T(row - 1, row - 1) + T(row, row);
			Scalar det = T(row - 1, row - 1) * T(row, row) - T(row - 1, row) * T(row, row - 1);
			VERIFY(4 * det > tr * tr);
		}
	}
}

template<typename MatrixType>
void
schur(int size = MatrixType::ColsAtCompileTime)
{
	// Test basic functionality: T is quasi-triangular and A = U T U*
	for (int counter = 0; counter < g_repeat; ++counter) {
		MatrixType A = MatrixType::Random(size, size);
		RealSchur<MatrixType> schurOfA(A);
		VERIFY_IS_EQUAL(schurOfA.info(), Success);
		MatrixType U = schurOfA.matrixU();
		MatrixType T = schurOfA.matrixT();
		verifyIsQuasiTriangular(T);
		VERIFY_IS_APPROX(A, U * T * U.transpose());
	}

	// Test asserts when not initialized
	RealSchur<MatrixType> rsUninitialized;
	VERIFY_RAISES_ASSERT(rsUninitialized.matrixT());
	VERIFY_RAISES_ASSERT(rsUninitialized.matrixU());
	VERIFY_RAISES_ASSERT(rsUninitialized.info());

	// Test whether compute() and constructor returns same result
	MatrixType A = MatrixType::Random(size, size);
	RealSchur<MatrixType> rs1;
	rs1.compute(A);
	RealSchur<MatrixType> rs2(A);
	VERIFY_IS_EQUAL(rs1.info(), Success);
	VERIFY_IS_EQUAL(rs2.info(), Success);
	VERIFY_IS_EQUAL(rs1.matrixT(), rs2.matrixT());
	VERIFY_IS_EQUAL(rs1.matrixU(), rs2.matrixU());

	// Test maximum number of iterations
	RealSchur<MatrixType> rs3;
	rs3.setMaxIterations(RealSchur<MatrixType>::m_maxIterationsPerRow * size).compute(A);
	VERIFY_IS_EQUAL(rs3.info(), Success);
	VERIFY_IS_EQUAL(rs3.matrixT(), rs1.matrixT());
	VERIFY_IS_EQUAL(rs3.matrixU(), rs1.matrixU());
	if (size > 2) {
		rs3.setMaxIterations(1).compute(A);
		VERIFY_IS_EQUAL(rs3.info(), NoConvergence);
		VERIFY_IS_EQUAL(rs3.getMaxIterations(), 1);
	}

	MatrixType Atriangular = A;
	Atriangular.template triangularView<StrictlyLower>().setZero();
	rs3.setMaxIterations(1).compute(Atriangular); // triangular matrices do not need any iterations
	VERIFY_IS_EQUAL(rs3.info(), Success);
	VERIFY_IS_APPROX(rs3.matrixT(), Atriangular); // approx because of scaling...
	VERIFY_IS_EQUAL(rs3.matrixU(), MatrixType::Identity(size, size));

	// Test computation of only T, not U
	RealSchur<MatrixType> rsOnlyT(A, false);
	VERIFY_IS_EQUAL(rsOnlyT.info(), Success);
	VERIFY_IS_EQUAL(rs1.matrixT(), rsOnlyT.matrixT());
	VERIFY_RAISES_ASSERT(rsOnlyT.matrixU());

	if (size > 2 && size < 20) {
		// Test matrix with NaN
		A(0, 0) = std::numeric_limits<typename MatrixType::Scalar>::quiet_NaN();
		RealSchur<MatrixType> rsNaN(A);
		VERIFY_IS_EQUAL(rsNaN.info(), NoConvergence);
	}
}

EIGEN_DECLARE_TEST(schur_real)
{
	CALL_SUBTEST_1((schur<Matrix4f>()));
	CALL_SUBTEST_2((schur<MatrixXd>(internal::random<int>(1, EIGEN_TEST_MAX_SIZE / 4))));
	CALL_SUBTEST_3((schur<Matrix<float, 1, 1>>()));
	CALL_SUBTEST_4((schur<Matrix<double, 3, 3, Eigen::RowMajor>>()));

	// Test problem size constructors
	CALL_SUBTEST_5(RealSchur<MatrixXf>(10));
}
